Question: The equation of a circle $C$ is $x^2+y^2-2x-16y+16 = 0$. What is its center $(h, k)$ and its radius $r$ ?
Explanation: To find the equation in standard form, complete the square. $(x^2-2x) + (y^2-16y) = -16$ $(x^2-2x+1) + (y^2-16y+64) = -16 + 1 + 64$ $(x-1)^{2} + (y-8)^{2} = 49 = 7^2$ Thus, $(h, k) = (1, 8)$ and $r = 7$.